Abstract
The subject of this paper is an accurate numerical method for solving the linear two-dimensional steady potential flow around a body which moves in a liquid of finite constant depth at constant speed and distance below the free surface. The differential equation is discretized by a second-order accurate finite difference scheme on a composite grid. The composite grid consists of two overlapping component grids; one curvilinear grid close to the body and one Cartesian grid which covers the surrounding liquid. To solve the problem numerically, the infinite domain is truncated to finite length. The inflow and outflow boundary conditions are formed by making an eigenfunction expansion of the solution ahead of and behind the body. Each eigenfunction is required to be bounded and satisfy the upstream condition at infinity. This is imposed by functional relations between the solution and its normal derivative at the inflow and outflow boundaries. The method is carefully validated and the computed solutions are found to be in very good agreement with existing results.
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